Reactance compensation



y 6, 1947- G. H. BROWN REACTANCE COMPENSATION Filed Aug. 25,1944 2 Sheets-Sheet l IN V EN TOR. alfilimwm a y 1947. G. H. BROWN I 2,419,985

REACTANCE COMPENSATION Filed Aug. 25, 1944 2 Sheets-Sheet 2 629013017. Brown Patented May 6, 1947 REACTANCE COMPENSATION George H. Brown, Princeton, N. J., assignor to Radio Corporation of America, a corporation of Delaware Application August 25, 1944,Serial No. 551,247

18 Claims. 1

This invention relates to reactance compensation and more particularly to improvements in the art of neutralizing the effects of the reactances which are unavoidably present in radio frequency power circuits. As is well known to those skilled in the art, the frequency band width throughout which a radio frequency transmission circuit operates efiiciently to transfer power is a function of the shunt reactances present in the circuit. Thus a radio frequency source of internal resistance R shunted by a capacitance C will develop across a load of impedance R a voltage which is at least 70 percent of its maximum value at any frequency within a band of width The center frequency In of the band Af depends upon the magnitude of inductance L connected across the source:

It is apparent that the greater the capacitance C, the narrower the band throughout which the system will transmit power efficiently.

The principal object of the present invention is to provide improved methods of and means for compensating the effects of reactance in radio frequency power circuits.

Another object is to provide improved methods of and means for obtaining broad-band operation of radio frequency power circuits.

A further object is to provide methods of and means for compensating the reactances of shortcircuited quarter wave line sections such as are used in line balance convertor systems, quarter wave supporting stubs and the like.

A still further object is to provide an improved coaxial transmission line structure wherein the inner conductor is supported on quarter wave stub lines, including means for compensating the reactances of said stub lines,

These and other objects will becomeapparent to those skilled in the art upon consideration of the following description with reference to the accompanying drawings, of which Figure 1 is a schematic circuit diagram of a power transmisslon circuit embodying the invention; Figure 2 is a group of graphs illustrating the effects of varying the characteristic impedance of one of the transmission line elements in the circuit of Figure 1; Figure 3 is a further group of graphs illustrating the design of the circuit of Figure 1;

Figure 4 is a schematic diagram of a stub supreactance across the'load I.

ported coaxial transmission line constructed in accordance witnprior art practice; Figure 5 is a schematic diagram of a stub supported coaxial line in accordance with the practice of the instant invention; and Figure 6 is a schematic diagram of a'stub supported open-wire line analogous to the coaxial line of Figure 5; Figure 7 is a modification of Figure 6; Figure 8 is a schematic diagram of a further type of power transmission circuit embodying the invention; and Figures 9 and 10 are modifications of Figure 8.

Referring to Figure 1, it is assumed that a load of impedance Z0 is to be energized from a source 3, also of impedance Z0 through a transmission line 5 having a characteristic impedance of Zn. In the absence of any further circuit elements, the load "I and line 5 will be matched to the source 3 at all frequencies, providing efficient transfer of power independently of frequency. It is assumed, however, that it is necessary to connect across the load I a transmission line section I, short-circuited at its end remote from the load I. It is well known that quarter wavelength shortcircuited transmission lines exhibit characteristics similar to those of parallel resonant circuits. Thus at the frequency at which the line 1 is onequarter wavelength long, a'veryhigh impedance, resistive in character, is presented across the load i. At lower frequencies; the line 7 acts like an inductance connected to the load I, while at higher frequencies the line 1 presents a capacitive As long as the reactance of the line I is very much greater in magnitude than the impedance Z0 of theload I, there is substantially no impedance mismatch caused by the presence ofthe line i. However,

at all frequencies outside of a certain. relatively narrow band, the reactance of the line I will be of the same order as the impedance Zn, or lower. At any of these frequencies, a major portion of the current from the source 3 will flow through the line 1, causingserious impedance mismatch and preventing efficient transfer of energy from the source 3 to the load I.

No great amount of energy is dissipated in the line 1 under the foregoing conditions. The current is reflected back down the line 5 to the source 3. Denoting the current transmitted by the source 3' as ii, and the reflected current i2, the absolute value of i isthe reflection coeillcient K. The degree of impedance match is commonly expressed in terms the impedance of the line 1 to the impedance of standing wave ratio R where of the load I. From such families of curves the I M flattest curve, corresponding to the curve C of R=m f Figure 2, may be selected to determine the cor- 1 root ratio Zc/Zo for providing optimum reactance Referring to Figure 2, the standing wave ratio compensation This has been done, and the on the line 5 a function of frequency, when sults are illustrated by the Curve E f Figure supplying the load 2 shunted by he line 7 with- The abscissa of the graph of Figure 3 is ZO/ZS' out compensation tie at 5 represented by the Solid where Z5 is the surge impedance of the quarter a Curve The represents the departure wave line sections 1 and II, and Z0 of the imn the resor frequency mi th i 1, t pedance of the load I. From the curve E the is )o is the reson t frequency or the line i and 7 proper Value of the impedance Zc in terms f the is the actual frequency of the energy being transload impedance Z0 may be Seheeted. Although the niitted. It is seen that at resonance the standing lines 5 1 H and 9 are illustrated schematically wave ratio is unity, indicating that no refiecin Figure 1 as paranel open w1re lines, it is to be tion occurs. At all other frequencies, R is less understood that any n of the above lines than 1, increasing with the departure from o. may be f coaxialeenstmctioh,

The curve of A, as well as the other curves of Denoting the electrical length of the line Figure 2, is based on the assumption that the tion 9 as p, and t of the lines 1 and H as 2 characteristic impedance of the line 7 is twice the impedance looking into h load from h the impedance of the load 5. end of the line section 9 i In accordance with the present invention, the 7 t t) 7 line 5 terminates in a line section 9 of one-half (1) z =e iff 1 1 1 i5 wavelength at the resonant frequency of the line do tan do 005 (PM) Sm PM I, and of impedance Zc. A quarter wave line H, The impedance looking into the line section 9 electricallyidentical with the line 1, is connected from its junction with the line 5 is Z Z cos /2-Z Z sin /2 tan p+jZ Z, sin /2 across the junction between the lines 5 and 9. Denoting the impedance at the end of the line 5, It is found that by adujsting the surge impedance looking into the line 9 and including the quarter Zc of the line section 9 to the proper Value, the wave line H as Zr,

1 1 1 3) Z ZF J' an (11/2) standing wave ratio may be maintained substan- H Denoting the conductive component of the admittially equal to 1 over a wide range of frequencies. tance The curves B, C and D of Figure 2 show how the 1 ratio R varies with frequency with values of 1.1

Z0, 1.2 Z0, 1.3 Zn respectively for the surge impedance Zc of the line section 9. It is seen that with as Gi:

Z=1.lZo, the standing wave ratio remains Denoting the susceptive component of higher than .9 throughout the range .57 f0 to 1.43 1

f0. With Zc:1.2 Z0, the ratio R remains substantially constant at unity from .75 in to 1.25 f0.

The preferred value for Zc probably lies someas Bi:

: [(Z Z3) Z5 sin /2) tan p ZiZE' cos /2) tan ZgZ,Z sin /2) cos /2) tan ,0 ZgZ Z sin /2 cos /Q] where between 1.1 and 1.2 Zn, providing a stand- Thus Zr, R1 and Xi may be computed for any ing wave characteristic intermediate those shown Values Z5, Z0 and Zc.

by curves B and C. Curve D show clearly that Z03 Z0 is outsid t pief 116d mm of talues for (I) Z.-=R.-+J

Families of curves similar to those of Figure 2 may be calculated and plotted for other ratios of The standing wave ratio R may be computed as mentioned above from the direct and reflected currents i1 and i2.

where A is a constant. The curves of Figure 2 are calculated by substituting the indicated values of Z0, Z and ZS in the above Equations 4, 5, and 6 to determine R1 and X1, which are substituted in Equations 8 and 9 to determine the currents 2'1 and ii for calculating the standing wave ratio.

By differentiating the expression for Bi (Equation 6) with respect to p, substituting p=1r radians, and setting and solving for Z0 in terms of Zn:

Z 2 M et Z Z Z: Z8 70 This represents the value of which provides zero rate of change of B1 with frequency. Equation is represented graphically by the line F of Figure 3. It is seen that the curve F deviates from the curve E by a varying amount, up to about 10 percent at This is accounted for by the fact that the curve which is flattest at in is not necessarily the flattest throughout an appreciable range. See Figure 2. Since the values of represented by the curve E were determined by inspection of families of curves like that of Figure 2, it is probable that the optimum value, for a given set of conditions, for the ratio lies somewhere between that indicated by the curves E and F of Figure 3.

The above described method of reactance compensation may be applied to the design of a stub supported transmission line. Referring to Figure 4, a coaxial stub supported line constructed in accordance with prior art practice comprises an outer conductor l3 and an inner conductor l5. In order to avoid the use of insulating materials for supporting the inner conductor 15, a plurality of quarter wave short-circuited stub lines are provided, with their outer conductors I! connected to the outer conductor l3, and their inner conductors I9 connected to and supporting the inner conductor 15. At the frequency at which the stub supporting lines are exactly onequarter wavelength, the impedances presented by the stubs are so great with respect to the characteristic impedance of the line l3, l5 that their shunting effect is negligible. At lower frequencies, the lines I1, I 9 present inductive reactances along the line [3, l5 and at higher frequencies, capacitive reactances. These reactances are neutralized to some extent by placing the stub lines at points 2| and 23, one-quarter wavelength apart along the line [3, l 5. At frequencies somewhat lower than it, the inductive reactance presented by the stub at the point 2| is substantially inverted by the quarter wave section between the points 2! and 23 to provide capacitive reactance at the point 23, which tends to cancel the inductive reactance presented by the other stub line at the point 23. Thus the system of Figure 4 will operate efiiciently throughout a band of frequencies, rather than only at the single frequency ft. The same principle may be applied to a stub supported parallel open-wire line.

Referring to Figure 5, a stub supported coaxial line in accordance with the instant invention is shown. This line will operate over a wider band of frequencies than that shown in Figure 4. A line section comprising inner and outer conductors 25 and 21 respectively is inserted in series in the line l3, IS. The section 25, 21 is one-half wavelength long at the frequency in, and the stubs I1, I9 are connected to the ends thereof. By proportioning the diameters of the conductors 25 and 21 to provide the proper surge impedance in accordance with the information illustrated graphically in Figure 3, the half wave line section and the supporting stubs are designed to introduce substantially no reflection throughout a relatively wide band of frequencies. It will be apparent that supporting sections such as that illustrated in Figure 5 may be placed at points along the line [3, l5 as far apart or as close together as dictated by mechanical consideration. A further possibility is to provide a stub at each half wavelength interval along the line l3, l5. In this case the diameters of the inner and outer conductors will remain constant throughout the length of the transmission line. However, the input and output impedances of the line will be somewhat lower than the characteristic impedance of the line itself.

As is the case with the prior art stub supported line of Figure 4, analogous parallel openwire lines may be constructed embodying the principles illustrated in Figure 5. Referring to Figure 6, an open-wire line comprising parallel conductors 4| includes a section 43 one-half wavelength long of characteristic impedance Zc, shunted at each end by quarter wave open-wire stubs 45, short-circuited at their lower ends, which rest on a supporting surface 41. The correct value of the impedance Z0 of the section 43 may be obtained by adjustment of the spacing between the conductors 43, as shown in Figure 6, or by using conductors in the section 43 which are of a different diameter from the conductors 4|.

Referring to Figure '7, a structure similar to that of Figure 6 is illustrated, in which the half wave conductors 43 are spaced the same as the conductors 4|, but are of smaller diameters to provide the correct value of Z0. Coaxial quarter wave stubs 49 are substituted for the open wire stubs 45 of Figure 6. Each of the stubs 49 com prises a conductor 59 surrounded by a conductive sleeve 52. The sleeve 52 is one-quarter wavelength long at the mean operating frequency and is connected at its lower end to the conductor 50. Four coaxial stubs 49 are required, one for each end of the conductors 43. Each stub operates like the stubs ll, [9 of Figure 5. The operation of the system of Figure 7 is like that of Figure 6.

A further application of the invention is illustrated in Figure 8. A radio frequency source 3, which may be a vacuum tube oscillator or amplifier, is to be coupled to a load I. It is assumed that the impedance of the source I is matched to that of the load I. A capacitance, represented by a capacitor 29, is shunted across the source 3. As stated above, the smaller the value of the capacitor 29, the broader the band throughout which energy can be transmitted to the load 5. The capacitor 28 is shunted by an inductor 31 to resonate at the center frequency ft of the band throughout which transmission is desired. A half wavelength line section 33 is connected at one end to the source 3. The other end of the line 33 is shunted by a quarter wave stub 35. A line 3'! is connected to the line 33 and across the stub and extends to the load 5. The line 3'! is designed to have a characteristic impedance Z equal to the impedance R of the load I. The characteristic impedance 25 of the stub 35 is made equal to where L is the inductance of the inductor 3i and C is the capacitance of the capacitor 29. The proper characteristic impedance Zc for the half wave section 33 may be determined from the curve E of Figure 3.

Referring to Figure 9, a capacitor 39 and an inductor 36, identical with the capacitor 29 and inductor 3|, may be placed at the end of the half wave section 33 instead of the stub 35 of Figure 8. The impedance Zc of the section 33 may be determined by using a value of with the curve E of Figure 2.

Figure illustrates a further modification,

which is equal to wherein stub lines 32, and 34, not necessarily onequarter wavelength long, but identical with each other, are substituted for the inductors 3| and 36 of Figure 9. The system of Figure 10 is otherwise identical with that of Figure 9 and is designed in the same manner.

Thus the invention has been described as an. improvement in the art of reactance compensation. A half Wavelength transmission line is connected to the point at which the reactance to be compensated appears, and is shunted at its other end by a reactance element substantially identical with that to be compensated. By adjusting the characteristic impedance of the half wavelength line in accordance with that of the reactance elements and the impedance of the transmission circuit, comp nsation is effected throughout a relatively wide band of frequencies. Several applications of the invention have been described. It is to be understood, however, that the invention may be used in numerous other situations where undesirable reactance is present. One such application is illustrated in copending U. S. patent ap plication Serial No. 550,566, filed by G. H. Brown and D, W. Peterson on August 22, 1944, and entitled Radio power division networks, wherein the reactance of a line balance convertor device is compensated.

The invention covered herein may be manufactured and used by or for the Government of the United States for any governmental purpose without payment to me or assigns of any royalty there- I claim as my invention:

1. In a radio frequency network including a load and a reactance element shunting said load, means for compensating the effects of said reactance element comprising a transmission line one half wavelength long at the center of the band of frequencies throughout which th system is to operate, connected at one end to said load, and a second reactance element substantially identical with said first reactance element connected to the other end of said line.

2. In a radio frequency network including a source and a reactance element shunting said source, means for compensating the effects of said reactance element comprising a transmission line one half wavelength long at the center of the band of frequencies throughout-which the system is to operate, connected at one end to said source, and a second reactance element substantially identical with said first reactance element connected to the other end of said line.

3. A radio frequency network including a source of radio frequency energy, a load, a resonant element shunting said load and resonant at the center of the band of frequencies throughout which the system is to operate, and means for compensating the reactance effects of said resonant element, comprising a transmission line substantially one half wavelength long at the center of the band of frequencies throughout which the system is to operate, with one of its ends connected to said load and the other of its ends connected to said source, and a second resonant element connected to said last mentioned end of said line and resonant at the center of the band of frequencies throughout which the system is to operate.

4. A radio frequency network including a source of radio frequency energy, a load, a resonant element shunting said source and resonant at the center of the band of frequencies throughout which the system is to operate, and means for compensating the reactance effects of said resonant element, comprising a transmission line substantially one half wavelength long at the center of the band of frequencies throughout which the system is to operate, with one of its ends connected to said source and the other of its ends connected to said load, and a second resonant element connected to said last mentioned end of said line and resonant at the center of the band of frequencies throughout which the system is to 0pcrate.

5. In a radio frequency network including a load of impedance Z0, shunted by an element which exhibits parallel resonant characteristics to energy of wavelength A, and has a surge impedance 25, a system for compensating the reactance of said element throughout a band of fre- 'quencies, comprising a transmission line of length M2 and surge impedance Zc, connected at one of its ends to said load, and a second element exhibiting parallel resonant characteristics identical with those of said first mentioned element, connected to th other end of said line, the surge impedance Z0 of said line being such as to satisfy the relation:

6. In a radio frequency network including a source of impedance Z0, shunted by an element which exhibits parallel resonant characteristics to energy of wavelength and has a surge impedance ZS, a system for compensating the reactance of said element throughout a band of frequencies, comprising a transmission line of length M2 and surge impedance Zc, connected at one of its ends to said source, and a second element exhibiting parallel resonant characteristics identical with those of said first mentioned element, connected to the other end of said line, the surge impedance Zc of said line being such as to satisfy the relation:

Z, 2 ga a oo) Z' Z,

7. In a radio frequency network including a load of impedance Z0, shunted by an element which exhibits parallel resonant characteristics to energy of wavelength A, and has a surge impedance ZS, a system for compensating the reactance of said element throughout a band of frequencies, comprising a transmission line of length M2 and surge impedance Z0, connected at one of its ends to said load, and a second element exhibiting parallel resonant characteristics identical with those of said first mentioned element, connected to the other end of said line, the surge impedance Zc of said line being such that the quantity has a value lying within the range of 90 percent to 100 percent of that of the quantity Z, 2 w re a 8. In a radio frequency network including a source of impedance Z0, shunted by an element which exhibits parallel resonant characteristics to energy of Wavelength A, and has a surge impedance ZS, a system for compensating the reactance of said element throughout a band of frequencies, comprising a transmission line of length \/2 and surge impedance Z0, connected at one of its ends to said source, and a second element exhibiting parallel resonant characteristics identical with those of said first mentioned element, connected to the other end of said line, the surge impedance Zc of said line being such that the quantity has a value lying within the range of 90 percent to 100 percent of that of the quantity Q) r e a 9. In a radio frequency network including a source of radio frequency energy, a load of impedance Z0, a transmission line section'connected to said load device, and having a length of an integra1 number of quarter wavelengths at the center of the band of frequencies throughout which the system is to operate and a surge impedance ZS, a system for compensating the reactance of said transmission line section, including a second transmission line section of one half wavelength and a surge impedance Zc connected at one of its ends to said load and at the other of its ends to said source, and a third transmission line section substantially identical electrically with said first transmission line section, connected to the source end of said half wave line, the impedances Z0, ZS and Zc being related as follows:

10. In a radio frequency network including a load, a source of impedance Z0, a transmission line section connected to said source, and having a length of an integral number of quarter wavelengths at the center of the band of frequencies throughout which the system is to operate and a surge impedance ZS, a system for compensating the reactance of said transmission line section, including a second transmission line section of one half wavelength and a surge impedance Zc connected at one of its ends to said load and at the other of its ends to said source, and a third transmission line section substantially identical electrically with said first transmission line section, connected to the load end of said half Wave line, the impedances Z0, Z5 and Z0 being related as follows:

-t co) 11. In a radio frequency network including a source of radio frequency energy, a load of impedance Z0, a transmission line section connected to said load device, and having a length of an integral number of quarter wavelengths at the center of the band of frequencies throughout which the system is to operate and a surge impedance 25, a system for compensating the reaotance of said transmission line section, including a second transmission line section of one half wavelength and a surge impedance Zc connected at one of its ends to said load and at the other of its ends to said source, and a third transmission line section substantially identical electrically with said first transmission line section, connected to the source end of said half wave line, the impedances Z0, Z5 and Zc being related so that the quantity has a value within the range of percent to percent of that of the quantity 12. In a radio frequency network including a source of radio frequency energy, a load of impedance Z0, a transmission line section connected to said source, and having a length of an integral number of quarter wavelengths at the center of the band of frequencies throughout which the system is to operate and a surge impedance 25, a system for compensating the reactance of said line section, including a second transmission line section of one half wavelength and a surge impedance Zc connected at one of its ends to said load and at the other of its ends to said source, and a third transmission line section substantially identical electrically with said first transmission line section, connected to the load end of said half wave line, the impedances Z0, Z5, and Z being related so that the quantity has a value within the range of 90 percent to 100 percent of that of the quantity 13. In a radio frequency network including a source of radio frequency energy, a load of impedance Z0, a transmission line section onequarter Wavelength long connected at one end to said load device, and short-circuited at its other end and having a surge impedance Z5, and a system for compensating the reactance of said transmission line section, including a second transmission line section of one half wavelength and a surge impedance Z0 connected at one of its ends to said load and at the other of its ends to said source, and a third transmission line section substantially identical electrically with said first transmission line section, with one end connected to the source end of said half wave line and its other end short-circuited, the impedances Z0, Z5 and Z0 being related so that the quantity transmission has a value within the range of 90 percent to 100 percent of that of the quantity:

' 2 w re 14. In a radio frequency network including a source of radio frequency energy, a load of impedance Z0, a transmission line section one-quarter wavelength long connected at one end to said source and short-circuited at its other end, and having a surge impedance Z5, and a system for compensating the reactance of said transmission line section, including a second transmission line section of one half wavelength and a surge impedance Zc connected at one of its ends to said load and at the other of its ends to said source, and a third transmission line section substantially identical electrically with said first transmission line section, with one end connected to the load end of said half wave line and its other end shortcircuited, the impedance Z0, Z5 and Z0 being related so that the quantity has a value within the range of 90 percent to 100 percent of that of the quantity:

15. A radio frequency power transmission system including a load of impedance Z0, a radio frequency source of impedance Z0, a transmission line havin a surge impedance Z0 connecting said load to said source, and a plurality of shortcircuited stub line sections of lengths M4 and surge impedance ZS connected to said transmission line at intervals along its length of \/2, wherein A is the wavelength at the center of the band of frequencies throughout which the system is to operate, and the impedances Z0, Z5, and Z0 are related so that the quantity has a value within the range of percent to percent of that of the quantity:

W st) Z, a

16. A stub supported coaxial transmission line of characteristic impedance Z0, including at least one supporting member comprising a half wavelength coaxial line section of characteristic impedance Zc provided with short-circuited quarter wave supporting stub lines of characteristic imedance 25 connected to each end thereof, wherein is within the range of 90 per cent to 100 percent w eY 1'7. In a radio frequency power system including a source of internal resistance R and a capacitance C, tuned to resonance at a frequency f by a shunt inductance L, a load of resistance R, broad band transmission means for coupling said source to said load including a transmission line of one half wavelength at the frequency 1 and of characteristic impedance Z0 connected between said load and said source, and a short-circuited transmission line of one-quarter wavelength at the frequency f and of characteristic impedance 25 connected across said load, wherein Z5 and Zc are related to R in such manner that is within the range of 90 percent to 100 percent of ing stub hues of characteristic impedance Z5 connected to each end thereof, wherein is within the range of 90 percent to 100 percent w ey 2T 2:

GEORGE H. BROWN.

REFERENCES CITED The following references are of record in the 5 file of this patent:

UNITED STATES PATENTS 

